Temperature dependence of the first pressure derivative of the isothermal bulk modulus for solid materials at zero pressure: Application to MgO

Because of the significance of the first pressure derivative of the isothermal bulk modulus ( K ′ T,0 ) at temperature, T , and zero pressure, a thermodynamic model was developed to calculate K ′ T,0 and its temperature derivative ∂ K ′ T,0 /∂ T . This model constructs a differential equation of K ′ T,0 with respect to temperature based on the well‐known empirical linear relationship of the Anderson‐Grüneisen parameter, δ T , and the compression ratio, η. By solving this differential equation, we derived both K ′ T,0 and ∂ K ′ T,0 /∂ T at a temperature, T , and zero pressure in terms of the known parameters of thermal expansivity, α, isobaric heat capacity, C P , and isothermal bulk modulus, K T at ambient pressure, and K ′ T at a reference temperature, T 0 , and ambient pressure. The reliability of this model was confirmed by comparing the modeled MgO results with previous data. This model will provide a powerful tool for determining the equation of state and the thermoelastic properties of solid materials at high temperatures and high pressures.